DECISION AND ORDER
LARIMER, District Judge.INTRODUCTION
Plaintiff, Raymond Cimino, commenced this action on November 18, 2002, asserting claims under 42 U.S.C. § 1983 and state law against the City of Rochester (“the City”) and two Rochester police officers, Mark Glaze and Michael Mareano. Plaintiffs claims arise out of an incident that occurred on July 26, 2001, when plaintiff was allegedly struck in the arm by a bullet fired by either Glaze or Mareano following a police chase of a truck being driven by plaintiff.
The original, pro se complaint sets forth three causes of action: (1) what appears to be a claim for assault and battery under state law; (2) a Fourth Amendment excessive-force claim brought under § 1983 against Glaze and Mareano; and (3) a § 1983 excessive-force claim against the City. The third cause of action alleges, inter alia, that Glaze’s and Marcano’s “use of excessive force was done ... pursuant to policy and/or custom of the City of Rochester and/or the City ratified their actions.” Complaint ¶ 47. It also alleges that then-Rochester Police Chief Robert Duffy “specifically approved of the actions taken by the individual Defendants in this case, and specifically approved of their indiscriminate and wild shooting at the truck and its occupants____” Complaint ¶ 49.
On September 29, 2004, without obtaining leave of court, plaintiff, having retained counsel, filed an amended complaint. The amended complaint adds as defendants Duffy (in both his individual and official capacities), three police officer “John Doe” defendants, and the Rochester Police Department (“RPD”). The proposed amended complaint also asserts five causes of action: (1) a Fourth Amendment excessive-force claim against Glaze and Mareano; (2) a due process claim against Glaze and Mareano under the Fifth Amendment; (3) a due process claim against Glaze and Mareano under the Fourteenth Amendment; (4) a claim against Glaze and Mareano for assault and battery; *171and (5) a § 1983 claim against the City, RPD, and Duffy for failure to adequately train, supervise and discipline the defendant police officers, or to prevent the shooting of plaintiff. The amended complaint also increases the ad damnum, clause from $450,000 compensatory and $300,000 punitive damages to $2,000,000 in compensatory damages, and an unspecified amount of punitive damages.
Defendants then moved to dismiss the amended complaint on the ground that the new claims, and claims against new defendants, are barred by the three-year statute of limitations for § 1983 actions. See Patterson v. County of Oneida, New York, 375 F.3d 206, 225 (2d Cir.2004) (statute of limitations applicable to claims brought under § 1983 in New York is three years). Plaintiff responded by moving for leave to amend the (original) complaint.
Since defendants answered the complaint in December 2002, plaintiff could not properly file an amended complaint without first obtaining leave of court. See Youn v. Track, Inc., 324 F.3d 409, 416 (6th Cir.2003) (“pursuant to [Rule 15], once the defendant has served a responsive pleading, a party may amend his complaint only by leave of court or with the consent of the adverse party”). I therefore will treat defendants’ motion to dismiss as their opposition to plaintiff’s belated motion for leave to amend.
DISCUSSION
I. Leave to Amend-General Standards
Rule 15(a) of the Federal Rules of Civil Procedure provides that leave to amend a pleading “shall be freely given when justice so requires.” The Second Circuit has stated that “justice does so require unless the [movant] is guilty of undue delay or bad faith or unless permission to amend would unduly prejudice the opposing party.” S.S. Silberblatt, Inc. v. East Harlem Pilot Block, 608 F.2d 28, 42 (2d Cir.1979).
The purpose of Rule 15(a) is to encourage disposition of litigation on the merits, rather than on procedural technicalities. Sanders v. Thrall Car Mfg. Co., 582 F.Supp. 945, 952 (S.D.N.Y.1983), aff'd, 730 F.2d 910 (2d Cir.1984). The Rule has been liberally interpreted by the Second Circuit, which has stated that it is “rare” that leave should be denied, especially when there has been no prior application to amend. Ricciuti v. New York City Transit Auth., 941 F.2d 119, 123 (2d Cir.1991) (citing Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962)). See also Kaster v. Modification Systems, Inc., 731 F.2d 1014, 1018 (2d Cir. 1984) (as long as the movant has “at least colorable grounds for relief, justice does ... require leave to amend”).
A court may deny leave to amend, however, where the amended pleading is considered futile. Foman, 371 U.S. at 182, 83 S.Ct. 227; John Hancock Mwt. Life Ins. Co. v. Amerford Int’l Corp., 22 F.3d 458, 462 (2d Cir.1994) (“[u]ndue delay and futility of the amendment, among other factors, are reasons to deny leave”); Health-Chem Corp. v. Baker, 915 F.2d 805, 810 (2d Cir.1990) (“where ... there is no merit in the proposed amendments, leave to amend should be denied”). An amendment is considered futile if the amended pleading fails to state a claim or would be subject to a motion to dismiss on some other basis. Dougherty v. Town of North Hempstead Bd. of Zoning Appeals, 282 F.3d 83, 88 (2d Cir.2002); McKinney v. Eastman Kodak Co., 975 F.Supp. 462, 465 (W.D.N.Y.1997).
II. Claims Against Duffy and the RPD
Before addressing the limitations issue, I note that to the extent that Duffy is sued in his official capacity, the claims against him are essentially claims against the City, so adding him as a defendant would change nothing. See Brandon v. Holt, 469 U.S. 464, 472, 105 S.Ct. 873, 83 L.Ed.2d 878 (1985). Likewise, plaintiffs claims against the RPD are in effect claims against the City. See Walker v. New York City Police Dep’t, No. 94 CV 3608, 1996 WL 391564, at *5 (E.D.N.Y. June 24, 1996) (holding that police department was not proper party to § 1983 action, and substituting city as defendant), aff'd, 205 F.3d 1327 (table), 2000 WL 233701 (2d Cir.2000). Accordingly, insofar as plaintiff seeks to amend the complaint to name as defendants the RPD and Duffy in *172his official capacity, plaintiffs motion is denied.
As to plaintiffs claim against Duffy in his individual capacity, plaintiffs motion for leave to amend is granted. Although the statute of limitations has run on plaintiffs § 1983 claim, Rule 15 of the Federal Rules of Civil Procedure permits a plaintiff, under certain circumstances, to amend his complaint to change or add a defendant after the statute of limitation has run. Davidson v. Conway, 318 F.Supp.2d 60, 62 (W.D.N.Y. 2004). In particular, Rule 15(c) provides that “[a]n amendment of a pleading relates back to the date of the original pleading when ... the claim or defense asserted in the amended pleading arose out of the conduct, transaction, or occurrence set forth or attempted to be set forth in the original pleading,” and
the amendment changes the party or the naming of the party against whom a claim is asserted ... and, within the period provided by Rule 4(m) for service of the summons and complaint, the party to be brought in by amendment (A) has received such notice of the institution of the action that the party will not be prejudiced in maintaining a defense on the merits, and (B) knew or should have known that, but for a mistake concerning the identity of the proper party, the action would have been brought against the party.
Here, the claim against Duffy clearly arises out of the occurrence that was set forth in the original pleading, ie. the shooting of plaintiff. In addition, the original complaint mentioned Duffy by name, and alleged that he “specifically approved” of Glaze’s and Marcano’s actions. Duffy is also deemed to have been on notice of plaintiffs lawsuit, since he and the City have an identity of interest. See, e.g., Jacobsen v. Osborne, 133 F.3d 315, 320 (5th Cir.1998) (city and police officers had sufficient identity of interest in false arrest case to permit relation back of amended complaint naming officers as defendants); O’Brien v. City of Grand Rapids, 783 F.Supp. 1034, 1039 (W.D.Mich. 1992) (relationship between original defendants-city and specific police officers-and proposed defendants-chief of police and police sergeant-was sufficiently close to support finding that proposed defendants had relatively prompt notice of contents of complaint at time it was served).
In addition, although at first blush there might seem to be no “mistake” here concerning Duffy’s identity, courts have not construed the term “mistake” in Rule 15 so narrowly. Rather, they have held that the “mistake” prerequisite should not be limited to cases of misnomer, but rather should be applied with an eye toward whether “the new party’s awareness that failure to join it was error rather than a deliberate strategy.” In re Integrated Resources Real Estate Securities Litigation, 815 F.Supp. 620, 644 (S.D.N.Y.1993) (quoting Advanced Power Sys., Inc. v. Hi-Tech Sys., Inc., 801 F.Supp. 1450 (E.D.Pa.1992)); see also Koal Indus. Corp. v. Asland, S.A., 808 F.Supp. 1143, 1157 (S.D.N.Y.1992) (stating that “Rule 15(c) is not limited to [literal] mistakes,” and that it “has been given a much broader reading” than misnomer); Sounds Express Int’l Ltd. v. American Themes and Tapes Inc., 101 F.R.D. 694, 697 (S.D.N.Y.1984) (“the rule clearly covers not only cases where a party has been misnamed or misdescribed, but also cases where there exists ‘a possibility that the plaintiff may have made a mistake in selecting the original defendants’ ”); 3 James Wm. Moore, Moore’s Federal Practice ¶ 15.19[3][d] (3d ed. 2005) (“A court should allow an amendment to relate back to add a defendant that was not named at the outset, but was added later when plaintiff realized that the defendant should have been named ...”).
In this case, the original complaint did contain allegations of wrongdoing by Duffy, even though he was not actually named as a defendant. Particularly since the original complaint was filed while plaintiff was pro se, I find that this is sufficient to constitute a “mistake” for purposes of Rule 15(c).
I realize that plaintiffs counsel filed then-notice of appearance on March 4, 2004, over four months prior to the expiration of the three-year limitations period. I see no indication of bad faith on counsel’s part, however, and, most importantly, no reason to think that defendants will be prejudiced by permitting the amendment. See Commander Oil *173Corp. v. Barlo Equip. Corp., 215 F.3d 321, 333 (2d Cir.2000) (“Parties are generally allowed to amend their pleadings absent bad faith or prejudice”), cert. denied, 531 U.S. 979, 121 S.Ct. 427, 148 L.Ed.2d 436 (2000); Block v. First Blood Associates, 988 F.2d 344, 350 (2d Cir.1993) (“Mere delay, ... absent a showing of bad faith or undue prejudice, does not provide a basis for a district court to deny the right to amend”) (internal citations and quotes omitted).1
III. Claims Against John Doe Defendants
Plaintiffs motion to add several John Doe defendants, however, must be denied. The law in the Second Circuit is clear that
Rule 15(c) does not allow an amended complaint adding new defendants to relate back if the newly-added defendants were not named originally because the plaintiff did not know their identities. Rule 15(c) explicitly allows the relation back of an amendment due to a “mistake” concerning the identity of the parties (under certain circumstances), but the failure to identify individual defendants when the plaintiff knows that such defendants must be named cannot be characterized as a mistake.
Barrow v. Wethersfield Police Dep’t, 66 F.3d 466, 470 (2d Cir.1995), as modified, 74 F.3d 1366 (2d Cir.1996). See also Tapia-Ortiz v. Doe, 171 F.3d 150, 152 (2d Cir.1999) (rule applies “even when a suit is brought by [a] pro se litigant”).
Thus, even if plaintiff had named the John Doe defendants in the original complaint, he could not now timely amend the complaint to add them by name. It would plainly be futile, then, to allow him to amend the complaint now to add any John Doe defendants, since any subsequent amendment identifying them by name would also be untimely.
IV. Addition of New Claims and Increase in Ad Damnum Clause
With one exception, the Court will permit plaintiff to amend the complaint to add new causes of action. Count II of the proposed amended complaint purports to assert a due process claim against Glaze and Marcano under the Fifth Amendment to the United States Constitution. The Fifth Amendment only applies to the states through the Fourteenth Amendment, however, see Ingraham v. Wright, 430 U.S. 651, 672-73, 97 S.Ct. 1401, 51 L.Ed.2d 711 (1977), and since Count III asserts an otherwise identical claim under the Fourteenth Amendment, Count II would be subject to dismissal as duplicative of Count III. See Cosby v. City of Oakland, No. C-97-0267, 1997 WL 703776, at *5 (N.D.Cal.1997) (“any Fifth Amendment claim is merely duplicative of the Fourteenth Amendment claims and, thus, is dismissed”). The other additional claims, however, all arise out of the same incident as the one set forth in the original complaint, see Fed. R.Civ.P. 15(c)(2), and will therefore be allowed.
As to the damage request, courts have held that an amendment increasing the amount of claimed damages should generally be allowed, absent some demonstrable prejudice to the defendant, which I do not see here. See, e.g., Camar Corp. v. Preston Trucking, Inc., No. CIV.A.96-40092, 1997 WL 345791, at *3 (D.Mass. June 20, 1997); Pesce v. General Motors Corp., 939 F.Supp. 160, 166 (N.D.N.Y.1996); Judy-Philippine Inc. v. S/S Verazano Bridge, 805 F.Supp. 185, 187 (S.D.N.Y.1992); cf. Ross v. Global Bus. Sch., Inc., No. 99 CIV. 2826, 2001 WL 1006656, at *7-8 (S.D.N.Y. Aug. 30, 2001) (leave to amend denied where discovery had been closed for a year, and amendment to increase damage request would require reopening of discovery related to alleged increase in plaintiffs lost wages). That amendment will also be allowed.
*174CONCLUSION
Defendants’ motion to dismiss (Dkt.# 12) is granted in part and denied in part. Defendants’ motion to dismiss plaintiffs claims against Robert Duffy in his official capacity, against the Rochester Police Department, and against the “John Doe” defendants is granted, and those claims are dismissed. Defendants’ motion to dismiss Count II of the amended complaint is also granted, and that cause of action is dismissed. In all other respects, defendants’ motion is denied.
Plaintiffs motion for leave to file an amended complaint (Dkt.# 16) is granted in part and denied in part. Plaintiff is hereby directed to file a second amended complaint within fifteen (15) days of the date of entry of this Decision and Order. The second amended complaint may assert all of the claims asserted in the amended complaint (Dkt.# 11), with the exception of the claims that have been dismissed by the Court, as recited in the preceding paragraph.
IT IS SO ORDERED.
. An amendment would also be futile if the proposed amended pleading fails to state a claim upon which relief can be granted. Dougherty, 282 F.3d at 88. Although "plaintiff faces a substantial challenge because failure to train claims are usually maintained against municipalities, not individuals,” Sanville v. McCaughtry, 266 F.3d 724, 739 (7th Cir.2001), the parties have not a